## Abstract

In this paper, we propose a particle-filter-based technique for the analysis of a reconstructed interference field. The particle filter and its variants are well proven as tracking filters in non-Gaussian and nonlinear situations. We propose to apply the particle filter for direct estimation of phase and its derivatives from digital holographic interferometric fringes via a signal-tracking approach on a Taylor series expanded state model and a polar-to-Cartesian-conversion-based measurement model. Computation of sample weights through non-Gaussian likelihood forms the major contribution of the proposed particle-filter-based approach compared to the existing unscented-Kalman-filter-based approach. It is observed that the proposed approach is highly robust to noise and outperforms the state-of-the-art especially at very low signal-to-noise ratios (i.e., especially in the range of $-5$ to 20 dB). The proposed approach, to the best of our knowledge, is the only method available for phase estimation from severely noisy fringe patterns even when the underlying phase pattern is rapidly varying and has a larger dynamic range. Simulation results and experimental data demonstrate the fact that the proposed approach is a better choice for direct phase estimation.

© 2016 Optical Society of America

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